Analytical solution of the system sensitivity equation associated with a linear model

In this paper an analytical derivation of the sensitivity of a linear model to a given parameter is presented. This derivation avoids the numerical solution of the system sensitivity equation associated with the model

$\text{dx/dt=Ax, x(0)=x}{}_0$

and thus reduces the amount of computer time and memory needed to make a comprehensive analysis. Moreover, because of its analytical nature no numerical errors of approximation are made.     

Relative stability of ecosystem linear models

A method to test the relative stability of ecosystem linear models is developed. This method uses the eigenvalue sensitivity to parameter perturbations to compute the relative stability of the model. The procedure is applied to the analysis of two models describing the ca;cium cycle in a forested watershed ecosystem and the magnesium cycle in a tropical rain forest respectively.     

The bootstrap and the jackknife in ecotoxicology or nonparametric estimates of standard error

A recently invented statistical method, the bootstrap, is used to verify whether a hypothesis, developed from a limited data set, would be valid if all possible data would have been available, i.e. this statistical method allows generalization to chemicals of the same class not included in the original analysis. The validity of the relation, hypothesized by Neely, between the water solubility of an organic chemical and the ratio of the acute fish LC50 at two different time periods has been tested. The hypothesis has been shown correct by first fitting a linear model with a geometric mean (GM) functional regression, which takes into account errors in both the independent and dependent variables, to compare observed and predicted ratios; the generality of the model has been tested by computing the confidence limits of the correlation coefficient, of the slope and intercept of the GM regression model using the bootstrap. The results show that the correlation between predicted and observed data is statistically significant within one standard deviation, but sometimes it may not be significant at the 95% confidence limit. Neely's model is probably correct but it might have a systematic bias which makes the theoretical ratio somewhat higher than the observed ratio.     

Identification of a dynamic lake model by the group method of data handling: An application to lake ontario

A revised algorithm of the group method of data handling (GMDH) is used to model and identify water quality dynamics in Lake Ontario. The state variables in the model are corrected chlorophyll a, volume-averaged over the top 20 m, and soluble reactive phosphorus in three layers, 0–20 m, 20–40 m and from 40 m to bottom. Inputs are the average quarterly temperatures for each layer and the total phosphorus loadings. Two kinds of model are developed: recursive and iterative; they are used to simulate long-term predictions for three different hypothetical rates of phosphorus loading. Results show that GMDH can be usefully employed to develop lake models with a very low expense of manpower and computer time. This exercise compares well with other large-scale modelling efforts of Lake Ontario, even if necessarily more limited in scope.     

Efficient algorithms for statistical estimation in compartmental analysis: Modelling 60Co kinetics in an aquatic microcosm

A mathematical model of radionuclide kinetics in a laboratory microcosm was built by systems identification techniques. Insight into the functioning of the system was obtained from analysis of the model. Methods employed have allowed movements of radioisotopes not directly observable in the experimental system to be distinguished. Results are generalized to whole ecosystems.     

Prenatal diagnosis of ventricular septal defect and overriding aorta at 14 weeks' gestation,using trans vaginal sonography

Two fetuses with heart abnormalities were detected by transvaginal sonography at 14 weeks of gestation. In the first fetus, a ventricular septal defect and an overriding aorta were detected and a diagnosis of tetralogy of Fallot was suggested. In addition, cystic hygroma and omphalocoele were visualized and the cytogenetic study revealed trisomy 18. In the second fetus, ventricular septal defect, pericardial effusion, and omphalocoele were detected.     

Identification of phosphorus dynamics in Kootenay Lake,Canada

This paper regards the use of system theory techniques in the development of models describing the phosphorus kinetics in fresh waters with the objective to understand the observed kinetics better in order to obtain indications on the design of future field experiments. Identification techniques have been applied to the data regarding 49 experiments on phosphorus cycling in Kootenay Lake, British Columbia, Canada, in order to determine the minimal number of compartments required to model the phosphorus dynamical behaviour. Canonical state-space models have then been identified both from raw and smoothed data. The parameters in these models do not have a direct physical meaning; they can, however, be identified from the measured data and the obtained models describe with good accuracy the considered kinetics. The identification of physical models has also been performed; in this case, however, only two compartments have been considered according to the results of the identifiability analysis of the complete model parameters. Results give further insight on the phosphorus processes and show that the complete phosphorus cycle through the four compartments described by Lean can be identified only when phosphorus cycles rapidly through the system.     

Adequacy of ecosystem models

A formal approach is developed to assess the adequacy of mathematical models to represent a given ecosystem. The procedure is based on the hypothesis that two or several models of an environment can be compared by using a vectorial approach: several model properties are analyzed and related to the model's capability to simulate the observed behaviour and to describe the ecosystem processes. The models are thus ordered from the standpoint of their adequacy. One preliminary model, a more recent one, and four lumped versions of the latter have been tested for adequacy. These models were developed by Wiegert and they describe the behaviour of an algal-fly community energetics in a thermal spring. Results obtained by our procedure agree with Wiegert's but some new points have been emphasized.